(a) Copy and complete the following table of values for (y = 9 cos x + 5 sin x) to one decimal place.
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° |
| y | 10.3 | -0.2 | -5.3 | -10.3 |
(b) Using a scale of 2cm to 30° on the x- axis and 2 cm to 1 unit on the y- axis, draw the graph of (y = 9 cos x + 5 sin x) for (0° leq x leq 210°).
(c) Use your graph to solve the equation: (i) (9cos x + 5sin x = 0); (ii) (9cos x+ 5sin x = 3.5), correct to the nearest degree.
(d) Find the maximum value of y correct to one decimal place.
Explanation
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° |
| y | 9 | 10.3 | 8.8 | 5 | -0.2 | -5.3 | -9 | -10.3 |
(b)
(c)(i) From the graph, (9cos x + 5sin x = 0 implies x = 119°)
(d) Maximum value of y = 10.3.